SCIENTIFIC PROGRAMS AND ACTIVTIES

Schedule

All the meetings will be held in the room HP 4351 (Macphail Room),
in Herzberg Laboratories. The room is next to the Main Office of the
School of Mathematic and Statistics. The phone number of the Main Office
is 613-520-2155.

On WEDNESDAY, Aug 16 the registration begins at 9:00, in the Main
Office of the School of Math and Stats (HP 4302), Herzberg Labs.

Wednesday Aug 16

10-11

Zlil Sela, Hebrew University Diophantine geometry over groups and the elementary theory
of a free group

Daniel Wise, McGill University
Nonpositively Curved Cube Complexes in Geometric Group Theory
Nonpositively curved cube complexes have come to occupy an increasingly
important role in geometric group theory. Surprisingly many of the
groups traditionally studied by combinatorial group theorists are
turning out to act properly on CAT(0) cube complexes. This is leading
to an increased and more unified understanding of these groups,
as well as the resolution of some of the algebraic problems that
were first raised in combinatorial group theory but were unapproachable
without geometric methods. We will survey groups acting on CAT(0)
cube complexes with an eye towards these recent developments.

16:00-16:45

Francisco F. Lasheras, University of Seville, Dpto. Geometria
& Topologia, Apdo. 1160, 41080-Sevilla (Spain)Some open questions on properly 3-realizable groups.
We recall that a finitely presented group is properly 3-realizable
if it is the fundamental group of a finite 2-polyhedron whose universal
cover has the proper homotopy type of a 3-manifold. We present a
quick review of properly 3-realizabler groups and their relation
to well-known conjectures and other properties for finitely presented
groups such as semistability at infinity and the WGSC and QSF properties.

17:00 - 17:45

Mihai D. Staic, SUNY at BuffaloLattice field theory and D-Groups.
We introduce D-groups and show how they fit in the context of lattice
field theory. To a manifold M we associate a D-group G(M). We define
the symmetric cohomology HSn(G, A) of a group G with coefficients
in a G-module A. The D-group G(M) is determined by the action of
p1(M) on p2(M) and an element of HS3(p1(M), p2(M)).

Thursday Aug 17

10-11

Zlil Sela, Hebrew University Diophantine geometry over groups and the elementary theory
of a free group

Stephen Pride, University of Glasgow On the residual finiteness and other properties of (relative)
one-relator groups
A relative one-relator presentation has the form P = <x, H;
R > where x is a set, H is a group, and R is a word on x±1
?H. We show that if the word on x±1 obtained from R by
deleting all the terms from H has what we call the unique max-min
property, then the group defined by P is residually finite if
and only if H is residually finite. We apply this to obtain new
results concerning the residual finiteness of (ordinary) one-relator
groups. We also obtain results concerning the conjugacy problem
for one-relator groups, and results concerning the relative asphericity
of presentations of the form P.

18:30

Dinner

Friday Aug 18

10-11

Zlil Sela, Hebrew University Diophantine geometry over groups and the elementary theory
of a free group

Bartosz Putrycz, Institute of Mathematics, University of
Gdansk Commutator subgroups of Hantzsche-Wendt groups.
Let a generalized Hantzsche-Wendt (GHW) group be the fundamental
group of a flat n-manifold with holonomy group Z2n-1. Let a Hantzsche-Wendt
(HW) group be a GHW group of an orientable manifold (n has to be
odd). We prove that for any HW group, with n > 3, its commutator
subgroup and translation subgroup are equal, hence its abelianization
is Z2n-1. We also give examples of GHW groups with the same property
for all n > 4. All these groups are examples of torsion-free
metabelian groups with abelianizations Z2k for k > 3.

Saturday Aug 19

9:30-10:30

Kanta Gupta, University of Manitoba
TBA

11:00-11:45

Volker Diekert, Universität Stuttgart
Coauthors: Markus Lohrey, Alexander MillerFree partially commutative inverse monoids.
Free partially commutative inverse monoids were first studied
in the thesis of da Costa in 2003, where, among others, the word
problem has been shown to be decidable.
We give a new approach to define free partially commutative inverse
monoids which is closer to standard constructions of Birget -
Rhodes and Margolis - Meakin. We use a natural closure operation
for subsets of free partially commutative groups - also known
as graph groups. We show that the word problem of a free partially
commutative inverse monoid is solvable in time O(n log(n)) on
a RAM.
The generalized word problem asks whether a given monoid element
belongs to a given finitely generated submonoid. In fact, we consider
the more general membership problem for rational subsets of a
free partially commutative inverse monoid, and we show its NP-completeness.
NP-hardness appears already for the special case of the generalized
word problem for a 2-generator free inverse monoid. It is quite
remarkable that the generalized word problem remains decidable
in our setting, because it is known to be undecidable for direct
products of free groups. So there is an undecidable problem for
a direct product of free groups where the same problem is decidable
for a direct product of free inverse monoids.
In the second part of the paper we consider free partially commutative
inverse monoids modulo a finite idempotent presentations, which
is a finite set of identities between idempotent elements. We
show that the resulting quotient monoids have decidable word problems
if and only if the underlying dependence structure is transitive.
In the transitive case, the uniform word problem (where the idempotent
presentation is part of the input) turns out to be EXP-complete,
whereas for a fixed idempotent presentation the word problem is
solvable both in linear time on a RAM and logarithmic space on
a Turing machine.
Our decidability result for the case of a transitive dependence
structure is unexpected in light of a result of Meakin and Sapir
(1996), where it was shown that there exist E-unitary inverse
monoids over a finitely generated Abelian group, where the word
problem is undecidable.
The talk is based on a joint work with Markus Lohrey Alexander
Miller which appears at MFCS 2006 (proceedings in the Springer
LNCS series).

12:00-1:00

Andrzej Szczepanski, University of Gdansk, Poland Spin structures on flat manifolds
Coauthors: G.Hiss (RWTH, Aachen)
Let G be a torsion free crystallographic group of dimension n
such that a flat manifold R^n/G is oriented one. We say that G
has a spin structure iff there exist a map e:G --> Spin(n)
such that l e = r, where l is a covering map Spin(n)-> SO(n)
and r is a holonomy map G --> SO(n). We shall present some
conditions for existing (or not) a spin structure on torsion free
crystallographic groups. For example for the space groups with
point groups of order four. We shall present many examples of
Bieberbach groups with and without spin structures.